Growth analytics / annualised return

Compound annual growth rate

Turn a beginning value, an ending value and a holding period into the single annual rate that connects them. The real, inflation-adjusted rate and the exact doubling time are reported alongside so nominal growth is never mistaken for purchasing power.

TrendCompounding upGrowth multiple2.50×Real multiple2.21×

CAGR

20.11%

Compound annual growth rate over the period

Total return

+150.00%

Cumulative change from start to end value

Real CAGR

17.18%

After 2.50% inflation (Fisher relation)

Doubling time

3.8 yr

Exact ln2/ln(1+g); the rule of 72 gives 3.6 yr

Growth path at the solved rate

The value implied by compounding the CAGR from the starting amount, with real (inflation-adjusted) values.

5.0 year horizon

Growth path at the solved rate
Year	Value at CAGR	Year-on-year growth	Real value
Year 0	$10,000	—	$10,000
Year 1	$12,011	+20.11%	$11,718
Year 2	$14,427	+20.11%	$13,732
Year 3	$17,329	+20.11%	$16,091
Year 4	$20,814	+20.11%	$18,856
Year 5	$25,000	+20.11%	$22,096

Real values deflate the nominal path by the entered inflation rate, which is what your money actually buys.

Start and end value

The two observations the growth rate is derived from, with the real end value for comparison.

Nominal vs real growth path

Compounding the solved rate forward, before and after inflation.

Canonical equations

The exact relationships implemented by this engine.

CAGR = (Vₙ / V₀)^(1/n) − 1 · the constant rate linking start and end value

g_real = (1 + g) / (1 + π) − 1 · Fisher relation; ≈ g − π for small rates

t₂ = ln 2 / ln(1 + g) · exact solution of (1+g)ᵗ = 2

t₂ ≈ 72 / (100g) · approximation, accurate to ~2% for 5–12% growth

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

CAGR is the single constant rate that carries a starting value to an ending value over a given number of years. It is the honest way to compare investments held for different periods, because it removes the length of the holding period from the comparison — but it says nothing about the path in between.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter the value at the start of the period.

Enter the value at the end. Any income taken out along the way should be added back for a total-return version.

Set the holding period in years. Use fractions for partial years.

Add an inflation assumption to see the real, purchasing-power growth rate.

Read the doubling time to sanity-check the rate against the rule of 72.

Use the growth-path table to see what smooth compounding at this rate would look like.

The formula

\mathrm{CAGR} = \left(\frac{V_n}{V_0}\right)^{1/n} - 1, \qquad g_{\text{real}} = \frac{1+\mathrm{CAGR}}{1+\pi} - 1, \qquad t_2 = \frac{\ln 2}{\ln(1+\mathrm{CAGR})}

Reference: Damodaran, "Investment Valuation", ch. 4; Fisher (1930) on real versus nominal rates.

Worked example

$10,000 growing to $25,000 over five years (default inputs)

Inputs

Beginning value $10,000.
Ending value $25,000.
Holding period 5 years.
Inflation 2.5% per year.

Calculation path

1
The growth multiple is 25,000 / 10,000 = 2.5×, a total return of 150%.
2
Annualise it: 2.5^(1/5) − 1 = 0.2011, so 20.11% a year.
3
Deflate for inflation: 1.2011 / 1.025 − 1 = 17.18% real growth.
4
Doubling time: ln 2 / ln 1.2011 = 3.78 years. The rule of 72 estimate is 3.58 years.

Result

CAGR 20.11% · total return 150% · real CAGR 17.18% · doubling time 3.78 years.

Interpreting the result

A CAGR of 20% sounds impressive until you notice it is being applied to a small base. The real rate is the one that matters for purchasing power: at 2.5% inflation, 20.11% nominal is 17.18% real, and the gap compounds over long horizons. Watch the doubling time as a gut check — a rate that doubles money in under four years is unusual and worth verifying against the actual price history.

Assumptions & limitations

Only the two endpoints matter. A volatile series and a smooth series with the same endpoints have the same CAGR.

No cash flows are added or withdrawn mid-period. Contributions need an IRR or time-weighted return instead.

Inflation is assumed constant over the whole period; real-world price levels move unevenly.

The holding period is measured in years; fractional years are allowed but assume smooth compounding within the year.

CAGR is a descriptive statistic, not a forecast. It does not extrapolate reliably.

Frequently asked questions

Is CAGR the same as average annual return?

No. CAGR is the geometric mean, which accounts for compounding; the arithmetic average overstates the rate actually achieved. A series that goes +50% then −50% has an arithmetic average of 0% but a CAGR of −13.4%.

Can CAGR be negative?

Yes. If the ending value is below the starting value, the CAGR is negative. The doubling time becomes undefined, which the engine reports rather than returning a spurious number.

Should I use CAGR or IRR?

CAGR for a single lump sum with no intermediate flows; IRR when money moves in and out during the period. IRR reduces to CAGR when there is exactly one outflow at the start and one inflow at the end.

How do dividends affect CAGR?

Add reinvested dividends to the ending value, or use a total-return index. Ignoring dividends understates the CAGR of income-producing assets, often by two to three points a year for equities.

Why does the rule of 72 differ from the exact doubling time?

The rule of 72 is a linear approximation to a logarithmic relationship. It is accurate to within about 2% for growth rates between 5% and 12%, and drifts at the extremes. The exact value here is ln 2 / ln(1+g).

How do I compare a 3-year CAGR with a 10-year CAGR?

Directly — that is the point of annualising. But compare risk too: a 20% CAGR over three years carries far more uncertainty than 8% over ten, and the shorter sample is more likely to be luck.